The survey, conducted on Thursday and Friday, found that 56 percent of respondents said Biden's conduct should not be viewed as disqualifying. Twenty-three percent said it should be, and 21 percent said they were unsure.

A majority of women and Democratic respondents said the allegations should not prevent him from running for president.

Biden is widely expected to declare his third White House bid, despite accusations from at least seven women who say he touched them at public events in ways that made them uncomfortable.

In a video posted to Twitter on Wednesday, Biden pledged to be "more mindful about respecting personal space." He did not directly apologize to his accusers, but he acknowledged that times have changed and that he would adjust his behavior.

"I don't see him as a threat. I think he's only a threat to himself," Trump told reporters at the White House.

A day earlier, Trump shared an edited video that poked fun at Biden for the recent controversy. The president posted the video, which features footage from a Biden's Wednesday statement, on his Twitter feed with the message "WELCOME BACK JOE!"

Biden on Friday made his first public appearance following the allegations, and he joked about the controversy during an address at the International Brotherhood of Electrical Workers conference.

The Hill-HarrisX survey found that 62 percent of Democratic respondents say the allegations of past behavior should not preclude him from being a 2020 candidate. Eighteen percent of Democrats said he should be disqualified, and 20 percent said they were unsure.

Thirty-two percent of GOP respondents said Biden should not run in light of the accusations against him, while 49 percent said the allegations should not prevent him from entering the crowded Democratic field of candidates. Nineteen percent said they were unsure.

Fifty-four percent of women said Biden should be allowed to run, despite the claims of inappropriate contact. Twenty-two percent said he should not launch a campaign, and 24 percent said they were uncertain.

Fifty-seven percent of men said Biden should not be disqualified, while 25 percent said he should. Eighteen percent were unsure.

The majority of independent voters -- 55 percent -- said they were OK with Biden running, even with the accusations. Twenty-one percent said he should be disqualified, with 24 percent voicing uncertainty.

Younger voters were much more likely to say Biden should not run. Thirty-one percent of adults under the age of 35 said Biden's past behavior was disqualifying. That view was shared by 25 percent of respondents between the ages of 35 and 49.

Just 19 percent of respondents between 50 and 64 said the former veep should be disqualified, with 16 percent of voters 65 and older saying the same.